Work

Inversion of noisy Radon transform by SVD based needlet

Year: 2008

Type: preprint

Abstract: A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in $L^p$ ($1\le p\le \infty$) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.0809.3332

Authors: Kerkyacharian, Gérard, Kyriazis, George, Pennec, Erwan Le, Petrushev, Pencho, Picard, Dominique

Institutions: Laboratoire de Probabilités et Modèles Aléatoires, University of Cyprus, University of South Carolina

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950087353

Cites: 24

Cited by: 2

Related to: 10